This invention relates to the field of molecular modeling, and more specifically to the design of molecular structures to achieve particular interactions with other molecules such as biological receptors and/or substrates.
Molecular design and modeling have been carried out by a variety of approaches, including conformational searching, energy minimization, energy calculation, normal mode analysis, molecular dynamics, stochastic dynamics and Monte Carlo simulations. These approaches all generally involve the estimation of one or more energy values for a molecule being modeled, and the prediction based upon this energy value of the physical properties and structure of the molecule. See, "Computer Assisted Modeling", National Academy Press, (1987). Different energy values will be incorporated into the model depending on their importance to the molecular properties of interest. Furthermore, more sophisticated models incorporate more energy values, while simpler models incorporate fewer energy values. The success of a particular modeling effort depends on the extent to which the energy values selected accurately and completely reflect a real molecule.
In modeling the behavior of molecules in solution, one important energy value is the solvation energy, E.sub.solvation. E.sub.solvation is generally viewed as the sum of three smaller energy components: the cavitation energy, E.sub.cav, the dispersion energy, E.sub.vdW, and the electrical polarization component of the solvation energy, E.sub.pol. The first two components are given by the summation across the atoms in the molecule of the atomic solvation parameter, .sigma., times the solvent accessible surface area of the atom, A, according to the equation EQU E.sub.cav +E.sub.vdW =.SIGMA..sigma..sub.i A.sub.i (Eq. 1)
Still et al., J. Am. Chem. Soc., 112, 6127-6129 (1990). The determination of E.sub.pol, however, is somewhat more difficult.
Classically, E.sub.pol (kcal/mole) for an electrical charge (q, in units of electron charge) at the center of a spherical particle of radius .alpha. (.ANG.) surrounded by a medium of dielectric .epsilon. is given by the Born equation: EQU E.sub.pol =-166(1-1/.epsilon.)q.sup.2 /.alpha. (Eq. 2)
M. Born, Z Physic, 1, 45 (1920). If the molecule being modeled is approximately spherical, and the charge is localized in the center of the molecule, the Born equation can be used to provide a reasonable value for E.sub.pol. Most molecules of interest do not fit these constraints, however. Because of this, a generalized Born equation has been developed to provide a value for E.sub.pol as follows: EQU E.sub.pol =-166(1-1/.epsilon.).SIGMA..sub.i .SIGMA..sub.j q.sub.i q.sub.j /(r.sub.ij.sup.2 +.alpha..sub.ij e**(-r.sub.ij.sup.2 /4.alpha..sub.ij.sup.2)).sup.0.5 (Eq. 3)
in which r.sub.ij is the separation between atoms i and j and .alpha..sub.ij is the mean Born radius of the atom i j pair. This equation provides a value for E.sub.pol provided that the effective Born radii .alpha. of each atom in the molecule is known so that .alpha..sub.ij can be calculated (e.g. .alpha..sub.ij =(.alpha..sub.i .alpha..sub.j).sup.0.5).
In the past, determination of the effective Born radius has been done, at best, using a semi-analytical approach such as that described in Still et al. J. Amer. Chem Soc. 112, 6127-6129 (1990), and the appendices thereto. This approach summed the Born electrostatic energies of a series of concentric shells of dielectric having thickness T beginning at the surface of atom being evaluated and extending outward to the van der Waals surface of the molecule. While this method is effective and has been incorporated in commercially available software for molecular modeling (MacroModel V 3.0), the calculation of effective Born radius for each atom is time consuming and limits the use of the approach to molecules of at most moderate size and complexity.
It is an object of the present invention to provide a more facile method of determining the effective Born radii of atoms in a complex molecular structure.
It is a further object of this invention to provide apparatus and methods which utilize the effective Born radii determined in accordance with the invention to predict the properties of molecular species.